Having an infinite decimal expansion is not what makes a number irrational. A rational number is any number that can be expressed as a fraction - that is, the words rational number and fraction are essentially synonymous.
$\pi$ is irrational because it cannot be expressed as a fraction - $22/7$ is a close approximation, but no fraction can ever exactly represent $\pi$. On the other hand, $1/3$, being a fraction, is rational by definition, irrespective of any infinite repeating decimal sequence.
The connection between irrational numbers and decimal sequences is this - if a number is irrational, it's decimal sequence cannot terminate, and furthermore the decimal sequence cannot be periodic, or repeating. This doesn't mean there can't be any pattern in the digits, just that they can't repeat themselves endlessly in uninterrupted fashion. A rational number, on the other hand, can have either a finite decimal expansion or an infinite expansion, but if the decimal expansion for a rational number is infinite, then it must be periodic, or repeating.
So the properties of the decimal expansions of rational and irrational number are a consequence of their definition in terms of representability by fractions, and not a definition in and of themselves.